1. Journal of Chromatography A, 1218 (2011) 6914–6921
Contents lists available at ScienceDirect
Journal of Chromatography A
journal homepage: www.elsevier.com/locate/chroma
Why ultra high performance liquid chromatography produces more tailing peaks
than high performance liquid chromatography, why it does not matter and how
it can be addressed
Patrik Peterssona,∗
, Patrik Forssenb
, Lena Edströmc
, Farzad Samied
, Stephen Tattertone
,
Adrian Clarkee,1
, Torgny Fornstedtb
a
AstraZeneca R&D Lund, SE-221 87 Lund, Sweden
b
Department of Chemistry and Biomedical Science, Karlstad University, SE-651 88 Karlstad, Sweden
c
Department of Physical and Analytical Chemistry, BMC Box 577, SE-751 23 Uppsala, Sweden
d
AstraZeneca Nordic Headquarters (ISMO), Södertälje, SE-151 85 Sweden
e
AstraZeneca R&D Charnwood, Loughborough, Leicestershire LE11 5RH, UK
a r t i c l e i n f o
Article history:
Received 13 December 2010
Received in revised form 23 May 2011
Accepted 7 August 2011
Available online 16 August 2011
Keywords:
UHPLC
HPLC
Isotherm
Simulation
Particle size
Translation
a b s t r a c t
The purpose of this study is to demonstrate, with experiments and with computer simulations based
on a firm chromatographic theory, that the wide spread perception of that the United States Pharma-
copeia tailing factor must be lower than 2 (Tf < 2) is questionable when using the latest generation of LC
equipment. It is shown that highly efficient LC separations like those obtained with sub-2 ␮m porous
and 2.7 ␮m superficially porous particles (UHPLC) produce significantly higher Tf-values than the corre-
sponding separation based on 3 ␮m porous particles (HPLC) when the same amount of sample is injected.
Still UHPLC separations provide a better resolution to adjacent peaks. Expressions have been derived that
describe how the Tf-value changes with particle size or number of theoretical plates. Expressions have
also been derived that can be used to scale the injection volume based on particle size or number of the-
oretical plates to maintain the Tf-value when translating a HPLC separation to the corresponding UHPLC
separation. An aspect that has been ignored in previous publications. Finally, data obtained from columns
with different age/condition indicate that Tf-values should be complemented by a peak width measure
to provide a more objective quality measure.
© 2011 Elsevier B.V. All rights reserved.
1. Introduction
In the pharmaceutical industry HPLC has long been established
as one of the main analytical techniques used controlling the quality
and consistency of the active drug substance, synthetic pre-cursors
(intermediates and starting materials), and drug product (dosage
form). A very central type of analysis is determination of the drug
related by-products and degradants. The data generated from this
type of analysis is of critical importance for the safety of the patients
as well as from an economical point of view. It is required that these
related impurities and degradants are determined down to 0.05%
(w/w) level of the drug substance. Consequently in LC it is neces-
sary to inject a relatively large amount of drug substance onto the
column to reach an acceptable signal to noise ratio for the related
∗ Corresponding author. Present address: Novo Nordisk A/S, Hagedornsvej 1, 2820
Gentofte, Denmark. Tel.: +45 307 921 46.
E-mail address: b.p.petersson@telia.com (P. Petersson).
1
Present address: Novartis Pharma AG, CH-4056 Basel, Switzerland.
impurities and degradants. This will, in most cases, result in an
overloaded asymmetric peak for the drug substance, a so-called
“shark fin” peak. Different measures have been defined for peak
asymmetry, the most frequently used measure within the pharma-
ceutical industry is the United States Pharmacopeia (USP) tailing
factor [1]:
Tf =
a + b
2a
(1)
where a and b are the front and back half widths at 5% of the max-
imum peak height. There is a common perception that Tf-values
larger than 2 not are acceptable [8]. During a recent large scale
implementation of UHPLC at AstraZeneca several users therefore
expressed concern when they observed Tf-values in the order of
4–5 when working with UHPLC. On the other hand, users working
in other projects did not observe any peak shape differences.
Asymmetric peaks are a concern in analytical chromatog-
raphy causing several problems. One such problem is a poor
signal to noise ratio as tailing will result in a broader peak with
lower response. A second problem is that it becomes difficult to
0021-9673/$ – see front matter © 2011 Elsevier B.V. All rights reserved.
doi:10.1016/j.chroma.2011.08.018

2. P. Petersson et al. / J. Chromatogr. A 1218 (2011) 6914–6921 6915
integrate the peak since it is unclear where the peak starts or ends
if the peak is fronting or tailing. A third reason is poor resolution
to adjacent peaks, small peaks eluting close to the overloaded peak
are swamped and becomes difficult/impossible to integrate or even
detect. For the analysis of related impurities and degradation prod-
ucts in pharmaceutical products it is mainly the latter problem that
is serious, i.e. if a peak cannot be detected it becomes impossible to
integrate.
Peak tailing has historically been blamed on many processes
that takes place inside or outside the column such as tailing
injection, slow detector response or extra-column contributions.
However, in modern LC applications, there are mainly two sources
for peak tailing: heterogeneous mass transfer kinetics [2–4] and
heterogeneous thermodynamics [5–7] with overloading due to a
nonlinear isotherm. Both types of peak tailing have been exten-
sively investigated using advanced computer simulations If the
peak tailing disappears at low analyte concentrations, this indi-
cates an absence of peak tailing due to heterogeneous mass transfer
kinetics.
Peak tailing due to heterogeneous thermodynamics assumes a
stationary phase that is covered with a large proportion of low-
energy adsorption sites and a small proportion of high-energy
adsorption sites [9]. Since the stationary phase contains fewer
strong sites these are much more easily overloaded, even at ␮M
concentrations. One classical example is reversed phase chro-
matography of protonated bases at low pH employing C18 columns
based on acidic silica. In this case the positively charged analytes
interact both with the hydrophobic C18 ligands (weak interac-
tions/sites) and with negatively charged silanol groups (strong
interactions/sites). It has also been suggested that strong inter-
actions/sites could constitute of repulsive interactions between
charged analytes, i.e. mutual repulsion of ionic species with the
same charge [10,11].
In the current work chromatographic theory, simulations and
experimental data have been combined to investigate how the
quality of the separation and the USP tailing factor changes when
translating methods between HPLC and UHPLC. Expressions have
been derived which explain how the Tf-value depends on parti-
cle size and number of theoretical plates. Expressions have also
been derived that describe how the injection volume can be scaled
against the same parameters to obtain equal Tf-value for both
techniques. Furthermore, the reasons why certain users observe
a higher Tf-value with UHPLC while others do not has been
addressed.
2. Theory
2.1. Isotherm determination by the CUT-ECP method
An isotherm displays the relationship between the adsorbed
solute concentration in the stationary phase vs. the solute concen-
tration in the mobile phase under constant temperature conditions
[12]. Depending on the adsorption mechanisms of the solute, the
isotherm curve can display different shapes. The isotherm shapes
have been described for gas–solid equilibrium [13,14], but these
can also be encountered in liquid–solid equilibrium applications.
The most common isotherm shape is the type I isotherm, which is
convex upwards and eventually reaches a saturation level in the
stationary phase. Highly overloaded chromatograms of a solute
that exhibits a type I isotherm behavior, often called Langmuir
isotherm, will display a right-angled triangular shape with a sharp
front and a diffuse rear [12]. In the present work a so-called
“bi-Langmuir” isotherm has been used for modeling, since this
isotherm has been shown to provide a good fit to experimental
data for the model substance used in the current study and for
related substances [7,6]. The bi-Langmuir isotherm can be written
as:
q(C) =
aIC
1 + bIC
+
aIIC
1 + bIIC
(2)
where q(C) is the concentration in the stationary phase corre-
sponding to the mobile phase concentration C, a and b are the
adsorption isotherm parameters for the two sites, I and II, respec-
tively.
There are many methods developed to experimentally obtain
adsorption isotherms, e.g. the inverse method, the frontal analy-
sis method (FA) and the elution by characteristic point method
(ECP) [12]. The latter is an experimentally simple and fast tech-
nique based on injection of a large and heavily overloaded pulse.
ECP has been previously studied regarding accuracy [15] and fur-
ther developed with great success [16], and was therefore chosen
for this study. This further developed ECP method is performed with
a so-called “cut-injection” technique (CUT-ECP), and gives nearly
identical adsorption isotherms as reference methods (FA) that are
known to be accurate. The accuracy originates from the genera-
tion of nearly rectangular injection profiles, obtained by turning
the injection valve back before the dispersed rear of the injection
plug reaches the column [16]. The dispersed tail of the injection
plug is thus left in the injection loop and never reaches the column.
The isotherm is then derived from the rear part of the band using
the equation:
q(C) =
1
Va
C
0
(VR(C) − VM − Vinj) dC (3)
where q(C) is the concentration in the stationary phase correspond-
ing to the mobile phase concentration C, Va is the volume of the solid
adsorbent, VR(C) is the elution volume corresponding to mobile
phase concentration C, VM is the column dead volume and Vinj is
the injected volume.
2.2. Simulation of chromatograms
To validate the acquired adsorption isotherm, elution profiles
are calculated numerically using a MATLAB program (MathWorks,
Natick, MA, USA) called “ChromSim Lite”, written in-house. In this
program, the chromatographic elution profiles are calculated in
Fortran 90 routines using the “Equilibrium-Dispersive” model and
the “Rouchon” upwind finite difference scheme. The model is based
on the differential mass balance equation:
∂C
∂t
+ ˚
∂q
∂t
+ uz
∂C
∂z
= Da
∂2C
∂z2
(4)
where uz is the linear mobile phase velocity, ˚ is the phase ratio, z
is the position in the column at time t and Da is the apparent disper-
sion constant. The input parameters to the simulation program are:
column length, column diameter, flow, stationary phase character-
istics (i.e. porosity, phase ratio, dead time or dead volume), injection
volume, the number of theoretical plates, solute concentration and
finally the adsorption isotherm parameters determined from the
CUT-ECP method. The calculated profiles are then overlaid on the
experimental profiles, visually inspected, and the degree of overlap
is calculated. An overlap of ≥95% can be considered as a good target
value [17,18]. Depending on the outcome of the visual inspection
and the degree of overlap, conclusions can be drawn considering
whether the adsorption isotherm model is correct or not.

3. 6916 P. Petersson et al. / J. Chromatogr. A 1218 (2011) 6914–6921
3. Experimental
3.1. Chemicals and reagents
Acetonitrile (Merck, Darmstadt, Germany) or methanol (JT
Baker, Deventer, The Netherlands) of gradient grade were used
for chromatography. Water was obtained from a Milli-Q system
(Molsheim, France). Diethyl ether (>99.9%), CH2Cl2, NaCl, NaOH,
H3PO4 (85%, w/w), H2SO4 (95–97%, w/w) and trifluoroacetic acid
of p.a. quality were obtained from Merck. KOH 1 N and metoprolol-
tartrate 99% from Sigma–Aldrich (Steinheim, Germany).
3.2. Preparation of different protolytic species of metoprolol
Metoprolol-base was produced by dissolving racemic
metoprolol-tartrate in a 0.1 M NaOH water phase (100 ml NaOH
water phase per gram of metoprolol-tartrate), and then shaking
this alkaline water phase with an equivalent (1:1) volume of
dichloromethane. This extracts the uncharged metoprolol-base
from the water phase to the organic phase. The dichloromethane
phase was then evaporated with a rotary evaporator and the
metoprolol-base crystals were dried and transferred to a dedicated
container. Metoprolol-HCl was produced by dissolving the above
produced metoprolol-base in dry diethyl ether (∼5 g metoprolol-
base in 100 mL diethyl ether), placing the solution on ice and then
bubbling HCl-gas through the diethyl ether solution. The HCl-gas
was produced by slowly dripping concentrated H2SO4 on NaCl and
gently carrying the generated gas over to the reaction vessel with
N2 as a carrier gas. When the metoprolol-HCl was precipitated the
crystals were subsequently poured onto a filter paper, washed by
vacuum filtration with cold dry diethyl ether and transferred to a
dedicated container.
3.3. Chromatography
Two types of systems were used in this study, Waters Acquity
UPLC systems controlled by Empower 2 (Waters, Milford, MA, USA)
and Agilent Technologies 1200 RRLC controlled by ChemStation
B.01.02 (Agilent Technologies, Waldbronn, Germany). The columns
utilized in the study were also obtained from Waters: BEH C18,
XBridge C18 and CSH C18, 50 mm × 2.1 mm I.D., with 1.7, 3.5 or
5 ␮m particle diameter. All columns were new as supplied by the
manufacturer and conditioned with at least 100 column volumes
prior to testing. A sampling rate of 40 Hz was employed to ensure
peak shape integrity. Conversion from absorbance to concentration
in chromatograms was performed by a non-linear calibration curve
for conc. vs. UV absorbance. Samples were dissolved in the isocratic
mobilephase used for elution.See figure captionsfor furtherdetails.
4. Results and discussion
4.1. Initial experimental results
Metoprolol chromatographed on 50 mm × 2.1 mm 1.7 ␮m
BEH/XBridge C18 and CSH C18 columns at 40 ◦C and pH 2.7 using
ACN as organic modifier were selected as model systems to study
how the peak shape changes as a function of particle size and
thus number of theoretical plates. Adsorption isotherms were
determined by the CUT-ECP method as described in the theory
section. Possible pH mismatch effects [19] were avoided by con-
verting the tartrate salt of metoprolol to its HCl salt. Subsequently
the isotherms obtained were validated by numerically calculat-
ing elution profiles and compare these with the corresponding
experimental elution profiles for a series of samples with differ-
ent concentrations (1 ␮M to 5 mM). Fig. 1 shows experimental and
simulated chromatograms for the CSH C18 column which isotherm
Volume [mL]
0.7 0.8 0.9 1.0 1.1
Concentration[mM]
0.00
0.02
0.04
0.06
0.08
0.10
Simulated
Experimental
Fig. 1. Simulated (dashed) and experimental (solid) chromatograms for an injection
of 5 ␮L of 2 mM metoprolol HCl dissolved in mobile phase on the 50 mm × 2.1 mm
1.7 ␮m CSH C18 column. The chromatograms coincide with a degree of overlap of
95% between 0.7 and 1.2 mL. Experimental conditions: flow 0.46 mL/min at 40 ◦
C,
mobile phase 7.5% ACN, 92.5% 3 mM potassium phosphate with pH 2.7. Simulation
parameters: porosity 0.90772, aI 12.67, bI 6.89 M−1
, aII 40.88, bII 2752.6 M−1
and
number of theoretical Plates 6 975 (measured for a non-overloaded injection of
3 ␮M).
gave the best predictions. The degree of overlap is 95% and repre-
sentative for what previously has been reported for this type of
modeling [9,17,18,20]. It should therefore be possible to use the
adsorption isotherm to investigate how the peak shapes and the
Tf-values change as a function of the number of theoretical plates
while keeping all other parameters constant. Thereby disturbing
factors, like column batch-to-batch variation, differences in instru-
mental contributions to extra column band broadening, etc., can be
avoided. Differences in friction heat are not covered by this model,
instead short columns and a relatively low flow rate, 0.5 mL/min,
has been employed to reduce the friction heat to not more than
∼2 ◦C for the 1.7 ␮m columns [21].
Since the peak tailing disappeared at low analyte concentra-
tion it could be concluded that the origin to tailing in this case was
related to heterogeneous thermodynamics (see above).
4.2. Simulations: the particle size effect on the tailing factor
After establishing a model which allows the prediction of peak
shape under overloaded conditions it was investigated how peak
shape and Tf-value changes in 50 mm × 2.1 mm columns packed
with 1.7, 3.5 and 5 ␮m particles. The number of theoretical plates
is approximately inversely proportional to the particle size, typi-
cally a 1.7 ␮m column produce 2× the number of theoretical plates
compared to a column of equal length packed with 3.5 ␮m parti-
cles [22,23]. It was therefore decided to use 7000, 3500 and 2500
theoretical plates for the simulations. Note that this is the num-
ber of theoretical plates obtained for symmetric Gaussian peaks at
low concentration. As shown in Fig. 2A and B the simulations sug-
gest that there is a linear increase of the Tf-value with increasing
number of theoretical plates. Also, with increasing number of the-
oretical plates, the apex of the peak is shifted to lower retention
volumes, the front becomes steeper and the peak width decreases.
A simulation based on a plate number of 1000 further accentuates
these trends (Fig. 2A and B). The Tf-values obtained for these sim-
ulated peaks shows differences between UHPLC, Tf = 6.3, and HPLC
separations, Tf = 3.7, which are in the same order as reported by

4. P. Petersson et al. / J. Chromatogr. A 1218 (2011) 6914–6921 6917
Fig. 2. (A) Simulated chromatograms for metoprolol chromatographed on 1.7, 3.5
and 5 ␮m versions of the CSH C18 column (only the 1.7 ␮m version was available
when the article was prepared). Included is also a curve corresponding to 1000
theoretical plates. (B) Tailing factor (solid), peak width at 5% peak height (dashed)
and retention volume for peak apex (dotted) determined for simulated curves as
function of number of theoretical plates. Conditions: 1 ␮L sample, otherwise as in
Fig. 1.
several users at AstraZeneca during the implementation of UHPLC,
i.e. 1.5–2×.
4.3. Experimental results: the particle size effect on the tailing
factor
In order to investigate if the same trends can be seen also for real
experimental data a metoprolol sample was chromatographed on
1.7, 3.5 and 5 ␮m versions of the BEH/XBridge C18 50 mm × 2.1 mm
column using the same UHPLC system and batch of mobile phases.
The BEH/XBridge material was used for the verification since the
CSH material only was available in 1.7 ␮m format. Trends are gen-
eral as long as the Langmuir-like adsorption isotherm relation is
the same for the different particles sizes (Section 4.7). The BEH
C18 and XBridge C18 columns are packed with the same pack-
ing material only the packing procedure and particle size differ.
To avoid memory effects which could affect the efficiency/peak
shape, previously unused columns were used. Each column was
carefully conditioned with at least 100 column volumes prior to
injection. As can be seen in Fig. 3, the experimental data from the
BEH/XBridge columns display the same trends as for the simulated
data for the CSH C18 columns, i.e. shorter retention volume for peak
Volume [mL]
1.4 1.5 1.6 1.7
Absorbance[mAU]
0
2
4
6
8
dp 1.7 µm, Tf 5.2
dp 3.5 µm, Tf 4.2
dp 5 µm, Tf 3.3
Fig. 3. Experimental chromatograms for metoprolol chromatographed on 1.7, 3.5
and 5 ␮m BEH/XBridge C18 columns. The volume scale has been shifted 0.01–0.1 mL
to align the front of the chromatograms. Conditions: flow 0.46 mL/min at 40 ◦
C,
mobile phase 11.8% ACN, 88.2% 3 mM potassium phosphate with pH 2.7 and 1 ␮L
sample of 2 mM metoprolol HCl dissolved in mobile phase.
apex, smaller peak width, higher peak height and sharper front with
decreasingparticlesizeandincreasingnumberof theoreticalplates.
There is a minor deviation in that the 1.7 and 3.5 ␮m versions show
a smaller difference in peak tailing and peak width. This could be
explained by variations in how good the columns have been packed
or batch to batch variations in the adsorption isotherms of the pack-
ing material. Nevertheless, the trends observed in simulated and
experimental chromatograms are the same, i.e. an increasing num-
ber of theoretical plates will result in increasing Tf-values, a peak
apex at lower retention, a narrower peak width and higher peak
height.
Clearly UHPLC and other highly efficient LC separations will pro-
duce much more asymmetric peaks with much higher Tf-values
than we are used to from HPLC employing 3 or 5 ␮m porous parti-
cles and conventional column lengths. How big the differences in
Tf-values are depend upon the particle size and the length of the
column.
4.4. Relationship between the particle size, number of theoretical
plates and tailing factor
As can be seen from Fig. 2B it is obvious that the relationship
between number of theoretical plates, N, and the tailing factor, Tf,
is linear, i.e.:
Tf = kfN + lT (5)
for some constants kT and lT. As can also be seen from Fig. 2B it is
reasonable to assume that
limN→0Tf ≈ 1 ⇔ lT ≈ 1 (6)
This means that the elution profile will tend to a Gaussian peak
when the number of theoretical plates decreases. To verify that Eqs.
(5) and (6) holds for an arbitrary bi-Langmuir system, i.e., that the
relationship between the tailing factor is linear and that the tailing
factor goes to 1 when the number of theoretical plates decreases,
a number of simulations using different system and adsorption
isotherm parameters were made.

5. 6918 P. Petersson et al. / J. Chromatogr. A 1218 (2011) 6914–6921
Fig. 4. Simulated UHPLC 1.7 ␮m (solid), HPLC 3.5 ␮m (dashed) and HPLC 5 ␮m
(dotted) chromatograms for metoprolol and 3 fictitious related impurities present
at 1% level. The fictitious related impurities were generated by making small
changes to the aII-value for metoprolol (aII = 36.5, 40.88, 44, and 47). Conditions:
100 mm × 2.1 mm column, 1 ␮L sample of 1 mM metoprolol HCl and 0.01 mM of
each related impurity dissolved in mobile phase, otherwise as in Fig. 1.
There is also the approximate relationship
N ∝
1
dp
⇔ N ≈
kp
dp
(7)
where dp is the particle size and kp is a constant. Using Eqs. (5)–(7),
the following relationship can be obtained:
Tf ≈
kTkp
dp
+ 1 (8)
The relationship in Eq. (8) can be used to estimate how the tailing
factor changes when going from a HPLC system to an UHPLC sys-
tem. It should be stressed, however, that Eq. (8) only is valid if all
parameters but the particle size is kept constant, i.e. anything else
that significantly affects the peak volume like changes to injection
volume, column dimensions and flow rate will also affect the degree
of overloading. Changes to column dimensions should therefore be
compensated by a scaling of injected sample volume and flow rate
(Section 4.6).
4.5. The particle size effect on the separation quality
Does a higher Tf-value, as a result of higher efficiency, have a
negative impact on the separation of adjacent peaks? As mentioned
in the introduction it is in most cases necessary to overload the drug
substance in order to reach acceptable signal to noise ratios for the
related impurities. This will affect the separation between the drug
substance and the related impurities eluting adjacent to it. To study
this, a simulation was made where fictitious related impurities,
present at low levels, have been placed close to the drug substance,
metoprolol. The peaks corresponding to the impurities were gen-
erated by making small adjustments to the adsorption isotherm
parameter aII in Eq. (2) for metoprolol. The UHPLC and HPLC chro-
matograms depicted in Fig. 4 shows that both peak height and
resolution for non overloaded symmetric Gaussian peaks increase
by ∼40% when doubling the number of theoretical plates as we go
from 3.5 ␮m HPLC (dashed line) to 1.7 ␮m UHPLC (solid line). This
improvement is what can be expected from linear theory since peak
height and resolution both are proportional to the square root of
the number of theoretical plates. The resolution between the asym-
metric metoprolol peak and the two adjacent impurity peaks are
also significantly better despite a much higher Tf-value for UHPLC,
3.7 vs. 2.4 for HPLC. The explanation is a reduction in peak width
for all peaks including the overloaded metoprolol peak. The latter
is reduced from 0.15 to 0.13 mL (peak width at 5% of peak height).
It would seem appropriate to develop new guidelines regarding
the Tf in UHPLC applications according to the findings, but as the
tailing due to overload depends on the type of adsorption isotherm,
general guidelines for all cases are hard to determine. Instead, a
higher Tf than 2 must be accepted and the respective separation
evaluated on a case-to-case basis.
4.6. Scaling to obtain the same selectivity and relative amount of
sample on the column
The results presented above do suggest that UHPLC should pro-
duce a higher Tf-value than the corresponding HPLC separation if
the same amount of sample is injected on both systems. During the
introduction of UHPLC at AstraZeneca this was not always observed
when users converted HPLC methods to UHPLC. There are several
potential explanations to this. One reason could be an inappropriate
translation of method: exactly the same mobile phases, tempera-
ture and packing material must be used. Anything that affects the
interactions between the analyte and the stationary phase (i.e. the
isotherm) may affect the symmetry of the peak. There is, for exam-
ple, a strong Tf response to changes in the ion strength of the mobile
phase, i.e. high ion strength will reduce tailing. Another potential
problem is that column brands may display a significant difference
in selectivity, retention and peak shape between different particle
sizes [24]. It is also of critical importance that the sample compo-
sition is the same and that the injection volume is scaled against
the column volume, i.e. Vinj,2 = Vinj,1VM,2/VM,1. If the column dimen-
sion is changed the flow rate needs to be scaled against the column
diameter to maintain the linear velocity, i.e. F2 = F1d2
2/d1
2.
If the translation is made for a gradient separation it is also
important to maintain the selectivity by keeping the following ratio
constant for each segment in the gradient:
tGF
VM ˚
(9)
where tG is the gradient time for the segment, F is the flow rate
and ˚ is the span of the gradient segment (fraction of the eluting
solvent, e.g. ACN). Consequently if the linear velocity is increased
to utilize the flatter van Deemter curves generated by UHPLC it will
be necessary to compensate this by reducing the gradient time.
Since the number of theoretical plates has a large impact on the
Tf-value it is also important to take extra column band broadening
into consideration when comparing columns and equipment. Extra
column band broadening aspects has been covered by Guiochon
et al. in a recent study [25].
4.7. Scaling of injection volume to obtain similar Tf-values
In order to obtain comparable Tf-values when changing par-
ticle size it is necessary to inject a significantly smaller volume
on the column with the smaller particle size even if the column
dimensions are the same.
To derive general expressions that describes how injection vol-
ume and peak height (apex concentration) depends on particle size
when the tailing factor is kept constant calculations were made for 3
very different systems. The parameters for these systems are given
in Table 1.
For each system, 40 simulations were done with the number
of theoretical plates, Nx, varied between 1000 and 8000. For 1000
theoretical plates 1 ␮L was injected and for the other number of the-
oretical plates the injection volume, Vinj, was adjusted so the tailing

6. P. Petersson et al. / J. Chromatogr. A 1218 (2011) 6914–6921 6919
Table 1
System parameters used for derivations.
Parameter System 1 System 2 System 3
Column length, L [mm] 50 250 150
Column diameter, d [mm] 2.1 4.6 4.6
Flow, F [ml/min] 0.46 1.5 1.0
Porosity, ε 0.92389 0.7697 0.581612535
Sample concentration, Cinj [mM] 2 150 150
Adsorption isotherm parameters
aI 12.67 20 15.04
bI [M−1
] 6.89 120 102.3
aII 40.88 – 4.21
bII [M−1
] 2752.6 – 42.78
factor, Tf, is the same as for 1000 plates. For the each simulation the
injection volume and peak height were recorded.
To derive an expression describing how the adjusted injection
volume, e.g. the one that keeps the tailing factor constant, depends
on the particle size the following calculations were made.
The injection volume, Vinj, 1 ␮L for 1000 theoretical plates, and
the corresponding tailing factor, was treated as a reference case and
to examine how many theoretical plates, Nx, that is required for a
smaller injection volumes to have the same tailing factor as in the
reference case (Fig. 5A). The noise in Figs. 5, 6 and 8 is related to dis-
cretization, the number of points in the simulated chromatograms.
In order to fit curves to the data the following nonlinear variable
transformation was used,
f (Nx, Vinj) =
1
Nx
(10)
this transformation is displayed in Fig. 5B. An appropriate non-
linear transformation was found using an in-house written
software which automatically evaluates all permitted non-linear
transformations of certain types.
A line f(Nx, Vinj) = k · Nx, with parameter k, was fitted to the trans-
formed variables and the equation for the corresponding curve in
Fig. 5A could then be written,
Nx =
1
kVinj
(11)
As previously mentioned,
Nx ≈
kp
dp
(12)
where dp is the particle size and kp is a constant. A combination of
Eqs. (11) and (12) gives,
Vinj ≈ ˜kdp where ˜k =
1
kpk
(13)
i.e. assume that for a column with particle size dp,1 and number of
theoretical plates Nx,1 the injection volume Vinj,1 will give a tailing
factor Tf. To have the same tailing factor for a column with particle
size dp,2 and number of theoretical plates Nx,2 one should use the
injection volume Vinj,2 where,
Vinj,2 ≈
dp,2
dp,1
Vinj,1 ⇔ Vinj,2 ≈
Nx,2
Nx,1
Vinj,1 (14)
In order to evaluate this expression the tailing factor for injection
volumes calculated according to Eq. (13) was compared to the tail-
ing factor for the used reference case (Vinj,1 = 1 ␮L, Nx,1 = 1000) in
Fig. 6.
To our knowledge the derivation of Eq. (14) is the first example
published which describes how translations of systems with over-
loaded asymmetric peaks can be performed with maintained peak
asymmetry. An aspect ignored in previous publications dealing
with translations between HPLC and UHPLC. Note that for systems
with different dimensions the scaling described in Sections 4.6 and
4.7 needs to be combined.
Fig. 7 shows chromatograms simulated for metoprolol chro-
matographed on 1.7 and 3.5 ␮m versions of the CSH C18 column
with injection volumes scaled to give to give either identical peak
height (i.e. peak apex concentration) or identical Tf-values. It should
be noted that the peak height is not constant when the injection
1000
2000
3000
4000
5000
6000
7000
8000
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Injection volumeV inj [µL]
A
NumberoftheoreticalplatesNx[-]
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Injection volumeV inj [µL]
f(Vinj,Nx)x10-3
B
Fig. 5. (A) How the number of theoretical plates, Nx, depends on the injection vol-
ume, Vinj, for systems 1 (triangle), 2 (box) and 3 (circle) and the corresponding fitted
curves (system 1 solid, system 2 long dash and system 3 short dash). (B) How the
transformed variables in Eq. (10) depend on the injection volume, Vinj, for systems
1–3 and the corresponding fitted curves.

7. 6920 P. Petersson et al. / J. Chromatogr. A 1218 (2011) 6914–6921
1
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
1000 2000 3000 4000 5000 6000 7000 8000
Number of theoretical plates N x [-]
TailingfactorTf[-]
Fig. 6. How the tailing factor, Tf, varies with the number of theoretical plates, Nx,
for systems 1–3 when the injection volume is calculated according to Eq. (14). The
lines are the tailing factor for the reference case Vinj = 1 ␮L, Nx = 1000.
volume is calculated according to Eq. (14), how it varies is shown
in Fig. 8.
In order to fit curves to the data the following nonlinear variable
transformation was used in analogy to what previously was shown
for Eq. (10).
f (Nx, Cmax) = −
N
3/4
x
V
1/2
inj
(15)
A line f(Nx, Cmax) = k · Nx, with parameter k, is fitted to the trans-
formed variables and the equation for the corresponding curve in
Fig. 8A can then be written,
Cmax =
1
k2 Nx
(16)
Fig. 7. Simulated chromatograms for metoprolol chromatographed on 1.7 and
3.5 ␮m versions of the CSH C18 column with injection volumes scaled to give to
give identical peak height or identical Tf-values (Eq. (14)). Conditions: As in Fig. 2.
0.005
0.015
0.025
0.035
0.045
0.055
0.065
0.075
0.085
1000 2000 3000 4000 5000 6000 7000 8000
Number of theoretical plates N x [-]
PeakheightCmax[mM]
Fig. 8. How the peak height, Cmax, varies with the number of theoretical plates, Nx,
for systems 1–3 (symbols) and the corresponding fitted lines when the injection
volume is calculated according to Eq. (14).
A combination of Eqs. (12) and (16) gives,
Cmax ≈ ˜k dp where ˜k =
1
k2 kp
(17)
i.e. assume that for a column with particle size dp,1 and number
of theoretical plates Nx,1 the injection volume Vinj,1 will give peak
height Cmax,1. For a column with particle size dp,2 and number of
theoretical plates Nx,2, using the injection volume Vinj,2 calculated
according to Eq. (14), the corresponding peak height Cmax,2 will be,
Cmax ≈
dp,2
dp,1
Cmax,1 ⇔ Cmax ≈
Nx,2
Nx,1
Cmax,1 (18)
4.8. The effect of column age and condition on the tailing factor
Even for translations where an appropriate scaling had been
performed certain users reported higher Tf-values for UHPLC and
others did not. One likely explanation turned out to be related to the
previous history and condition of the columns used. This was clearly
indicated when analyzing the same sample on 6 different UHPLC
systems equipped with 6 different BEH C18 50 mm × 2.1 mm
1.7 ␮m columns, with different age and in different condition, using
the same batch of mobile phase. The obtained Tf-values ranged
from 1.8 to 2.9. The columns with the “best” Tf-value (1.8–2.1) had
been used for 1257–2121 injections whereas the highest Tf-values
(2.8 − 2.9) were obtained on columns used for 8–86 injections. A
comparison of the chromatographic profiles, Fig. 9, shows that the
columns with the lowest Tf-values were the columns which dis-
played the broadest peaks and, in one case, even a shoulder. Since
the instruments are used as walk-up systems, where a number
of users analyze a variety of samples on the same column/system
using a range of pre-programmed methods, it was not possible to
identify to which extent these columns have been exposed to dif-
ferent samples and mobile phases. Nevertheless, the results clearly
show that the condition of the column has a critical importance
when comparing Tf-values. It also shows that a low tailing fac-
tor not necessarily means a better separation since the columns
with the narrowest peaks actually displayed the highest Tf-values.
This suggests that Tf-values need to be complemented by a peak
width measure in order to provide a more objective judgment of
the quality of the separation.

8. P. Petersson et al. / J. Chromatogr. A 1218 (2011) 6914–6921 6921
Volume [mL]
0.82 0.84 0.86 0.88 0.90 0.92 0.94 0.96 0.98 1.00
Normalizedabsorbance[-]
0.0
0.2
0.4
0.6
0.8
1.0
Tf 2.9
Tf 1.8
Fig. 9. A proprietary basic drug analyzed on 6 different UHPLC systems equipped
with 6 BEH C18 50 mm × 2.1 mm 1.7 ␮m columns with different history and condi-
tion, i.e. used for different number of injections (8–2121) and exposed to different
mobile phases and samples. The volume scale has been shifted 0.03–0.1 mL to align
the apex of the chromatograms. The absorbance scale has been normalized to 1 (max
absorbance 324 mAU). Experimental conditions: flow 0.3 mL/min, 60 ◦
C, 60% MeOH,
0.1% (v/v) trifluoroacetic acid. Sample: 8 ␮L of 0.1 mg/mL of the drug dissolved in
mobile phase.
5. Concluding remarks
The results presented in this study challenge the wide spread
perception that Tf-values >2 are not are acceptable. Highly effi-
cient LC separations like those obtained with sub-2 ␮m porous and
2.7 ␮m superficially porous particles produce significantly higher
Tf-values than the corresponding 3 ␮m separations when the same
amount of sample is injected. Still these separations provide a bet-
ter resolution than the corresponding 3 ␮m separations, i.e. UHPLC
provides a better separation than HPLC despite significantly higher
Tf-values. Expressions have been derived that show how the tail-
ing factor varies with the particle size or the number of theoretical
plates. Unfortunately it is difficult to state a general guideline since
the peak shape is highly dependent on the type of adsorption
isotherm (of which there are numerous) for each substance and
separation system. Instead, a higher Tf than 2 must be accepted for
UHPLC and the respective separation evaluated on a case-to-case
basis.
Identical Tf-values can be obtained if a smaller amount of sam-
ple is injected on the more efficient UHPLC system. Expressions
have been derived that show how injection volumes should be
scaled based on particle sizes or number of theoretical plates
to obtain identical Tf-values. An aspect that has been ignored
in previous publications dealing with translations between HPLC
and UHPLC. Such scaling will result in a lower peak height on
the UHPLC system but might still be acceptable since the res-
olution between the overloaded peak and adjacent peaks are
improved.
Finally, data obtained from columns with different age and back-
ground indicates that the Tf-values should be complemented by a
peak width measure, i.e. the condition of the column will have a
large impact on the number of theoretical plates and consequently
also the Tf-value.
Acknowledgement
Waters for supplying the prototype CSH C18 column.
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